1. Auditorium Acoustics 1. Sound propagation (Free field)
Free field: the sound source is small enough to be considered a point source, located outdoors away from reflecting surfaces
Intensity is proportional to 1/r2, where r is the distance from the source
Pressure is proportional to 1/r
Pressure is halved as the distance doubles
There is a 6 dB drop in sound pressure & intensity level as the distance doubles
Indoors free fields only exist in anechoic rooms (echo-free)

2. 1a. Sound propagation (Indoors)
Indoors, sound travels only a short distance before encountering walls and other obstacles
These obstacles either reflect of absorb sound according to the acoustic properties of the room
The reflection patterns are determined by the curvature of the surface
Reflection Surfaces

3. 2. Direct, early and reverberant sound
Direct sound traveling in air (344 m/s) would reach a listener in an auditorium after a time of 20 to 200 ms depending on the distance from the source
Shortly after, the same sound would reach the listener from various reflecting surfaces
Early sound - any of the first group of reflections arriving within 50 to 80 ms
After the early sounds, reflections arrive thick and fast from all directions
These reflections are smaller and closer together, merging after a time into reverberant sound

4. Interesting: A simple acoustical analysis of a room can be done by examining the nature of the direct, early and reverberant sound produced in that room
2a. Direct sound
In auditoriums, some sounds are non-directional: sounds that radiate essentially with the same intensity in all directions
Others, such as upper range frequencies of brass instruments, are directional
For low frequencies, localization is done based on the slight time difference in the time of arrival
For high frequencies, localization occurs through the difference in sound level caused by the sound shadow

5. 2b. Early sound 2c. Reverberant Sound
Rapidly varying early sounds are heard as reinforced direct sound if they reach the listener within 50 ms
For slowly varying early sounds, the limit is 80 ms
Precedence effect
The ear continues to deduce the direction of the source from the arrival of the first sound if successive sounds:
arrive within 35 ms
have spectra and time envelopes similar to the first sound
are not too much louder than the first
2c. Reverberant Sound
Reverberation sound in low levels reinforces the direct sound
However, excessive reverberation sound causes a loss of clarity

6. 3. Characteristics of reverberant sound
If the source emits continuous sound, the reverberant sound builds until an equilibrium level is reached.
This equilibrium reverberant level is reached when the rate at which energy is supplied by the source is equal to the rate at which the sound is absorbed.
When the sound source stop, the reverberant sound falls off at a constant rate until it is inaudible.
If the sound source were impulsive, an equilibrium state is never achieved.

7. 3. Characteristics of reverberant sound (continued)
If sound energy would be uniformly distributed throughout the room, its decay would follow an exponential curve
This would produce a straight line curve for the sound pressure level
c) In auditoriums, decay curves tend to have two different reverberation times
This may indicate an insufficient distribution of sound and can lead to a feeling of “dryness” in a hall even though the final reverberation time is within acceptable limits
d) Spikes in the decay curves result from storage of sound energy in resonances

8. 4. Reverberation time (RT or RT60)
The reverberant sound in an auditorium dies away with time as the sound energy is absorbed by multiple interactions with the surfaces of the room. In a more reflective room, it will take longer for the sound to die away and the room is said to be 'live'. In a very absorbent room, the sound will die away quickly and the room will be described as acoustically 'dead'. But the time for reverberation to completely die away will depend upon how loud the sound was to begin with, and will also depend upon the acuity of the hearing of the observer.
To have a reproducible parameter to characterize an auditorium which is independent of the intensity of the test sound, it is necessary to define a standard reverberation time in terms of the drop in intensity from the original level, i.e., to define it in terms of relative intensity.
Definition:
Reverberation time is usually defined as the time it takes for the sound level to decrease by 60 dB or double the time it takes for a 30 dB decrease

9. 4a. Reverberation time (Why 60dB?)
The choice of the relative intensity to use is of course arbitrary, but there is a good rationale for using 60 dB since the loudest crescendo for most orchestral music is about 100 dB and a typical room background level for a good music-making area is about 40 dB. Thus the standard reverberation time is seen to be about the time for the loudest crescendo of the orchestra to die away to the level of the room background. The 60 dB range is about the range of dynamic levels for orchestral music.

10. 5. Calculation of the reverberation time (Sabine formula)
Sound energy in the room depends on
the power of the source
the volume of the room
The rate at which that energy is absorbed depends on:
the area and absorption coefficients of all the surfaces in the room
Reverberation time (RT):
Generally, large rooms have longer reverberation times than do small rooms!
K – constant
V – volume of the room
A – absorption (effective surface area)
For a room with solid walls, which absorb very little sound, and an open window of area A, the reverberation constant is:

11. 5a. Absorption (effective surface area)
We can model rooms similarly to modeling the window of area A
We can assume an absorption coefficient, a, which depends on the amount of sound power absorbed
So any material having surface area S can be said to have A = Sa
Total absorption of the room is found by adding up the contributions from each surface exposed to the reverberant sound
Sometimes absorption is expressed in sabins or metric sabins
One sabin is the absorption of one square foot of open window

12. Absorption coefficients

13. This calculation leads to an unrealistically long reverberation time
Furnishings in room will contribute a substantial fraction of the total absorption
People are also good absorbers of sound

14. 5b. Air Absorption:
m – coefficient that depends on frequency, temperature and humidity
Air absorption is usually neglected in calculations of reverberation times for auditoriums, but for large enclosures it may become significant.
Air absorption is greater for high frequencies and is dependent upon air temperature and relative humidity
Air absorption m per cubic meter:
Air at
2000 Hz
4000 Hz
8000 Hz
20°C, 30% RH
0.012
0.038
0.136
20°C, 50% RH
0.010
0.024
0.086

15. 5c. Empty and occupied room
Measurements of sound decay in a classroom (Jesse) showed that the sound intensity level in decibels dropped off linearly with time.
Since decibels are a logarithmic quantity, this implies an exponential decay of the sound.
These plots can be extrapolated to give reverberation times for the room, which amount to about 0.5 s for the empty room and about 0.4 s for the occupied room.

16. 6. What is a desirable reverberation time?
The optimum reverberation time for an auditorium or room of course depends upon its intended use.
Around 2 seconds is desirable for a medium-sized, general purpose auditorium that is to be used for both speech and music.
A classroom should be much shorter, less than a second.
A recording studio should minimize reverberation time in most cases for clarity of recording.
The reverberation time is strongly influenced by the absorption coefficients of the surfaces, but it also depends upon the volume of the room as shown in the Sabine formula. You won't get a long reverberation time with a small room.

17. 6a. What is a desirable reverberation time (continued)?

18. Examples:
Vienna, Musikvereinsaal : 2.05 seconds
Boston, Symphony Hall: 1.8 seconds
New York, Carnegie Hall: 1.7 seconds
The most outstanding auditoriums show significantly longer reverberation times for low frequencies.
Reverberation time is a familiar auditorium characteristic
Though hard to quantify in a single measure, a fair indication of the “liveness” of a hall is given by the reverberation time of the mid frequencies (500 –2000 Hz)

19. Concert halls
A concert hall is considered “intimate” if the delay time between direct and first reflected sounds is less than 20 ms
Sometimes reflecting surfaces are suspended from the ceiling
A study has shown listeners prefer concert halls in which ceilings are sufficiently high so that the first lateral reflection reaches the listener before the first overhead reflection
Other studies have shown that if the total energy of the lateral reflections is greater than that of the overhead reflections, the hall has a “spatial responsiveness” or “spatial impression”